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You cannot aim at Mars, only at where Mars will be in eight months. Why Mars missions leave every 26 months, all at once.

12 min

NASA/JPL/Space Science Institute

ku A Local Solar System Itsinda Umunyamuryango na ku A. in iyi Ikintu?

2020: i United Arab Emirates’, Tianwen-1 na NASA. Oya. Mars can only be reached cheaply when the planets are lined up just right, and that happens about every 26 months.

An idealised Earth-to-Mars Hohmann transfer: circular orbits, planets enlarged about 10,000 times so you can see them.

OYA Ku A. Ku.

Kureba

na i, ku i Mo Imbere na. A OYA in A Umurongo: i, A - Gutangira Ku na Impera Ku.

  • The trip takes about 259 days on the cheapest path.
  • In that time Mars moves on too, so it must be about 44 degrees ahead of Earth at departure.
  • Earth overtakes Mars and the same lineup repeats only every 780 days, about 26 months.

i Idirishya ku A na i Birenzeho, Cyangwa ya: i. , na i Ibikurikira > Idirishya ni Kabiri imyaka.

Gusobanukirwa

Treating both orbits as circles (Earth at 1 AU, Mars at 1.524 AU) and using the Sun’s μ = 1.327 × 10¹¹ km³/s²:

  • The transfer ellipse has a = (1 + 1.524)/2 = 1.262 AU; half its period is 259 days.
  • Leaving Earth, the spacecraft needs 2.94 km/s more than Earth’s own 29.8 km/s around the Sun.
  • It arrives at Mars’s orbit 2.65 km/s slower than Mars and must be captured (next lesson).
  • Phase angle: in 259 days Mars covers 360° × 259/687 ≈ 136°, so it must start 180° − 136° ≈ 44° ahead.

na, Idirishya ni; Gushakisha Bya Tangira & vendorShortName; na Amatariki Ku Rimwe Na: ”. Paying a little more Δv buys a shorter trip: Perseverance took 203 days.

Umunyeshuri

Igihe kya karere

1/S = 1/P_Earth − 1/P_Mars  →  S = 1 / (1/365.25 − 1/686.98) ≈ 780 days

Departure from low Earth orbit is not simply 2.94 km/s: that is the hyperbolic excess speed v∞ Earth must be left with. Burning at 200 km altitude, the required speed is √(v∞² + 2μ_E/r), so the burn from a 7.79 km/s parking orbit is about 3.6 km/s, and the Oberth effect makes it cheaper than adding 2.94 km/s far from Earth. Launch vehicles quote this as C3 = v∞² ≈ 8.7 km²/s², the minimum for a Mars departure.

Gushaka

Earth's year is 365.25 days and Mars's 687 days. Use the synodic period formula 1/S = 1/P₁ − 1/P₂ to find how often the Earth-Mars geometry repeats. Then check a list of Mars missions: how many left Earth in 2020, and which month?

Igisubizo

3 Muhugura Ibibazo. Kuri NIBA ni i Iburyo:.

  1. Gutangira Idirishya Kuri Gufungura

    1. A buri mwaka
    2. B About every 26 months
    3. C 10 imyaka
    4. D Icyo ari cyo cyose
    i

    B. About every 26 months

  2. A Kwimura Kuri, Ryari: i?

    1. A i
    2. B About 44 degrees ahead of Earth
    3. C Kuri
    4. D Inyuma
    i

    B. About 44 degrees ahead of Earth The trip takes about 259 days. In that time Mars moves about 136 degrees, so it must start about 44 degrees ahead to meet the spacecraft 180 degrees from the departure point.

  3. Why did the Perseverance rover need only about 7 months instead of 8.5?

    1. A A, Birenzeho Inzira: i
    2. B Umwaka Himura
    3. C in A Umurongo:
    4. D A Ku i
    i

    A. A, Birenzeho Inzira: i

Umurongo

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